KABUL: An air strike on a hospital in the Afghan city of Kunduz on Saturday left three Doctors Without Borders staff dead and dozens more unaccounted for, the medical charity said, with North-Atlantic Treaty Organization (Nato) conceding United States (US) forces may have been behind the attack.

The Medecins Sans Frontieres (MSF) facility is seen as a key medical lifeline in the region and has been running "beyond capacity" in recent days of fighting that saw the Taliban seize control of the provincial capital for several days.

"At 2:10am local time... the MSF trauma centre in Kunduz was hit several times during sustained bombing and was very badly damaged," it said in a statement.

Three MSF staff are confirmed dead and more than 30 are unaccounted for.

The medical team is working around the clock to do everything possible for the safety of patients and hospital staff.

Kunduz has seen heavy fighting since Taliban insurgents stormed the provincial capital on Monday — the first major city to be captured by insurgents since 2001.

Read: 'Northern Afghan city of Kunduz collapses into hands of Taliban'

At the time of the bombing, 105 patients and their caregivers and more than 80 international and local MSF staff were in the hospital, the charity said.

Nato said US forces may be behind the strike.

"US forces conducted an air strike in Kunduz city at 2:15am... against individuals threatening the force," a Nato statement said.

"The strike may have resulted in collateral damage to a nearby medical facility. This incident is under investigation."

The MSF trauma centre in Kunduz is the only medical facility in the region that can deal with major injuries.

As fighting spreads in neighbouring Badakhshan, Takhar and Baghlan provinces, concerns are mounting that the seizure of Kunduz was merely the opening gambit in a new, bolder Taliban strategy to tighten the insurgency's grip across northern Afghanistan.

Afghan forces, backed by Nato special forces and US air strikes, have been going from house to house in Kunduz in a bid to flush out insurgents in the city.

The Taliban's offensive in Kunduz, their biggest tactical success since 2001, marks a major blow for Afghanistan's Western-trained forces, who have largely been fighting on their own since last December.

Civilian and military casualties caused by Nato forces have been one of the most contentious issues in the 14-year campaign against Taliban insurgents, provoking harsh public and government criticism.

In a statement, the Taliban accused "barbaric American forces" of deliberately carrying out Saturday's strike, which "killed and wounded tens of doctors, nurses and patients."

US-led Nato forces ended their combat mission in Afghanistan last December, though a 13,000-strong residual force remains for training and counter-terrorism operations.

But there has been an escalation in air strikes by Nato forces in recent months despite the drawdown.